GOST: A Geometric-Optical Model for Sloping Terrainsfaculty.geog.utoronto.ca/Chen/Chen's homepage... · 2000s withtheaddition of radiative transferschemes toaddress the complex multiple

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014 5469

GOST: A Geometric-Optical Modelfor Sloping Terrains

Weiliang Fan, Jing M. Chen, Weimin Ju, and Gaolong Zhu

Abstract—GOST is a geometric-optical (GO) model for slopingterrains developed in this study based on the four-scale GO model,which simulates the bidirectional reflectance distribution function(BRDF) of forest canopies on flat surfaces. The four-scale GOmodel considers four scales of canopy architecture: tree groups,tree crowns, branches, and shoots. In order to make this modelsuitable for sloping terrains, the mathematical description for theprojection of tree crowns on the ground has been modified toconsider the fact that trees grow vertically rather than perpen-dicularly to sloping grounds. The simulated canopy gap fractionand the area ratios of the four scene components (sunlit foliage,sunlit background, shaded foliage, and shaded background) byGOST compare well with those simulated by 3-D virtual canopycomputer modeling techniques for a hypothetical forest. GOSTsimulations show that the differences in area ratios of the fourscene components between flat and sloping terrains can reachup to 50%–60% in the principal plane and about 30% in theperpendicular plane. Two case studies are conducted to comparemodeled canopy reflectance with observations. One comparisonis made against Landsat-5 Thematic Mapper (TM) reflectance,demonstrating the ability of GOST to model canopy reflectancevariations with slope and aspect of the terrain. Another compar-ison is made against MODIS surface reflectance, showing thatGOST with topographic consideration outperforms that withouttopographic consideration. These comparisons confirm the abilityof GOST to model canopy reflectance on sloping terrains over alarge range of view angles.

Index Terms—Canopy structure, geometric-optical (GO) mod-eling, radiative transfer, remote sensing, sloping terrains.

NOMENCLATURE

A Vertical projected area of a quadrat.B Vertical projected domain area.D Number of trees in domain B.G(θ) Projection of unit leaf areas.H Effective height.

Manuscript received February 4, 2013; revised October 25, 2013; acceptedOctober 30, 2013. Date of publication November 22, 2013; date of currentversion March 5, 2014. This work was supported in part by the NationalScience Foundation of China under Grant 41271352/D0106, by the NationalBasic Research Program of China under Grant 2010CB950704, and by theChinese Academy of Sciences for Strategic Priority Research Program underGrant XDA05050602.

W. Fan and W. Ju are with the Jiangsu Provincial Key Laboratory ofGeographic Information Science and Technology and with the InternationalInstitute for Earth System Science, Nanjing University, Nanjing, 210046,China.

J. M. Chen is with the Jiangsu Provincial Key Laboratory of GeographicInformation Science and Technology and with the International Institute forEarth System Science, Nanjing University, Nanjing, 210046, China. He is alsowith the Department of Geography and Program in Planning, University ofToronto, Toronto, ON M5S 3G3, Canada (e-mail: [email protected]).

G. Zhu is with the Department of Geography, Minjiang University, Fuzhou350108, China.

Digital Object Identifier 10.1109/TGRS.2013.2289852

h Tree height Ha +Hb +Hc.Ha Height of the lower part of the tree (trunk

space).Hb Height of cylinders.Hc Height of cones.L Leaf area index (LAI).Lo Mean LAI accumulated over the view or sun

path within one tree crown.Lt Clumping-adjusted projected tree crown area

index.m Mean number of trees in a quadrat.m1 Mean number of cluster per quadrat.m2 Cluster mean size.n Number of quadrats in domain B.Nt(λ) Gap number density function between

canopies.PG Probability of sunlit ground area in the view

directions.Pgap(θ) Gap probability within a tree at angle θ.Pig Probability of sunlit ground area.Pvg Probability of viewing ground area.Pvg_r Probability of viewing ground area for ran-

dom tree distribution.Pvg_c Probability of viewing ground area for clus-

tered tree (Neyman distribution).PT Probability of viewing sunlit foliage.P (x) Poisson distribution.PN (i;m1;m2) Neyman type-A distribution.r Radius of the tree crowns.R Total reflectance.RG Ground reflectance.RT Tree reflectance.RZG Shaded ground surface reflectance.RZT Shaded tree surface reflectance.S The projected sloping quadrat area in the view

direction.s̄(θ) Mean path length within a crown.ta(θ) Tree crown surface area at θ.V Volume of a tree.Ws Mean width of element shadows cast inside

tree crowns.Wt Characteristic mean width of tree crowns pro-

jected to the ground.α Half apex angle.γE Needle-to-shoot area ratio.ΩE Clumping index for shoots.Ωt Clumping index for trees.λ Gap size.

0196-2892 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

5470 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 9, SEPTEMBER 2014

λmin Minimum gap size for having an illuminatedsurface.

φg Azimuth angle of the sloping background.φv View azimuth angle.φs Solar azimuth angle.φgv Relative azimuth angle between the viewer

and the sloping background.φsv Relative azimuth angle between the sun and

the viewer.φsg Relative azimuth angle between the sun and

the sloping background.θg Slope of the sloping background or zenith

angle of the sloping background.θ′s Solar zenith angle to the horizontal back-

ground.θs Solar incidence angle to the sloping back-

ground.θ′v View zenith angle to the horizontal back-

ground.θv View zenith angle to the sloping background.ξ Angle difference between the sun and the

viewer.SPT Percentage of sunlit points in viewed points.

I. INTRODUCTION

THE vegetation structure significantly affects its exchangesof matter and energy with the atmosphere, and therefore,

vegetation structural parameters are important basic data forglobal change research. Geometric-optical (GO) models, as onekind of forest reflectance models, are suitable for developingalgorithms for vegetation structural parameter retrieval becauseof their emphasis on vegetation structure and its interaction withradiative transfer processes in the canopy [1]–[4].

GO models have been well developed in the 1990s and early2000s with the addition of radiative transfer schemes to addressthe complex multiple scattering issues in the canopy [5]–[7].In recent years, the attention of many GO modelers have beenturned to the applications of GO models for retrieving struc-tural parameters such as LAI, clumping index, crown closure,and crown diameter [8]–[13]. Moreover, GO models are alsoused for canopy background reflectance retrieval [14]–[16],microwave modeling [17], and LiDAR analysis [18]–[20].

Many studies have shown that complex terrains stronglyinfluence the canopy reflectance detected by sensors [21]–[23].However, GO models are generally based on geometric re-lationships among solar zenith angle, view zenith angle, andrelative azimuth angle between the sun and the viewer. Theyare only suitable for retrieving structural parameters of forestsgrowing on flat terrains; however, forests are often found overcomplex terrains, which are particularly common in China.

A GO model consists of mathematical expressions of thecanopy structure and within-canopy radiative transfer pro-cesses. Complex terrains influence both expressions [24], [25].However, GO models usually only consider geometries ofcanopy structural components on a flat background [1], [2],[26]–[28]. Topographic corrections are generally used to reducethe topography effects on canopy bidirectional reflectance [22],

[29], [30]. However, these types of corrections aim only atimage angular normalization [31] and are not based on fun-damental mechanisms of the canopy radiative transfer and itsinteraction with the sloping background. Some studies havegone beyond these simple correction methods. For example,Schaaf et al. [24] attempted to establish a GO model suitable forsloping terrains based on the Li–Strahler GO model. This modeltransformed ellipsoidal crowns into spherical shapes in 3-Dspace to simplify the projection of these crowns on a slopingsurface. However, this approach is not suitable for crownsthat are different from the spherical shape. Combal et al. [31]pointed out that the model of Schaaf et al. [24] uses an implicitassumption that trees are perpendicular to the sloping surfaceand classified this type of models as Perpendicular to theGround Vegetation Model. In reality, most trees grow verticallywhether on a sloping surface. For applicability on complexterrains, it is necessary to establish a GO model consideringthe sloping canopy structure and radiative transfer mechanismsin the sloping canopy.

A GO model can be evaluated using observations against var-ious outcomes of the model, including 1) modeled reflectance[2], [27], [32]; 2) inverted canopy parameters [1], [10], [33],[34]; and 3) modeled canopy gap fractions [2], [27], [35].These outcome-based evaluations may not be sufficient becauseintermediate errors in producing an outcome could cancel eachother. With the development of computer technology, 3-Dvirtual canopy modeling [36]–[38] could be an effective wayto evaluate not only the outcome but also the intermediatemodeling results, such as the fractions of the sunlit and shadedfoliage and background. This new evaluation tool has allowedus to evaluate GOST in its various development stages.

In this paper, we focus on the development of a GO modelsuitable for sloping terrains (GOST) based on the four-scaleGO model [27] developed for flat terrains. GOST considers asloping canopy structure with trees growing vertically ratherthan perpendicularly to sloping surfaces. We make a compar-ison between GOST and a 3-D virtual computer model to provethat GOST has the ability to simulate the canopy gap fractionand area ratios of the four scene components (sunlit foliage,sunlit background, shaded foliage, and shaded background).The reflectance retrieved from a Landsat Thematic Mapper(TM) image and MODIS images are used to evaluate GOSTperformance.

II. MODEL DESCRIPTION

The reflected signals received by sensors are assumed to becomposed of signals from four scene components: sunlit foliage(PT ), sunlit ground (PG), shaded foliage (ZT ), and shadedground (ZG). The total canopy reflectance is

R = RT · PT +RG · PG +RZT · ZT +RZG · ZG (1)

where PT and PG are the sunlit components that intercept thedirect sunlight, and ZT and ZG are the shaded componentsreceiving only the diffuse radiation from the sky and scatteredradiation in the canopy. RT , RG, RZT , and RZG are thereflectance factors of the four scene components in GOST.

FAN et al.: GOST: A GEOMETRIC-OPTICAL MODEL FOR SLOPING TERRAINS 5471

Fig. 1. Coordinate system of photon interaction with a canopy on a slopingbackground. E, S, W, and N are the east, south, west, and north directions to thehorizontal ground. Z is the vertical direction to the horizontal ground. Z’ is thevertical direction to the sloping ground.

Here, the vegetation and background components in the viewdirection will be first separated based on the gap fraction, andthe four scene components will then be separated on slopingterrains.

A. Determining the Coordinate System for a Sloping Canopy

GO models, such as the four-scale GO model, assume thattrees are perpendicular to the background surface. The projec-tion of tree crowns on the background is described using thesolar zenith angle (θ′s), view zenith angle (θ′v), and relativeazimuth angle between the sun and the viewer (φsv) for thehorizontal surface. In GOST, the projection of forest scene com-ponents on sloping terrains is described using additional an-gles, including the solar incidence angle to the sloping surface(θs, cos(θs) = cos(θg) cos(θ

′s) + sin(θg) sin(θ

′s) cos(φsg)),

view incidence angle to the sloping surface (θv, cos(θv) =cos(θg) cos(θ

′v) + sin(θg) sin(θ

′v) cos(φgv)), and slope (θg)

and aspect (φg) (see Fig. 1).

B. Tree Distribution

The canopy gap size and gap fraction distributions are de-termined by the tree distribution. Chen and Leblanc [27] stud-ied both the random Poisson distribution and the nonrandomNeyman type-A distribution [39] for describing the tree distri-bution. The results showed that the Neyman type-A distribu-tion is better than the Poisson distribution in capturing a treedistribution pattern in a boreal forest. However, the Poissondistribution can be used as a backup approach when detailedtree distribution data are lacking. These two distributions arealternatively used in GOST, and other types of distributions canalso be used to replace them. In GOST, a study area is dividedinto a number of quadrats in order to obtain a statistical treedistribution. The Poisson distribution is

P (x) =e−mmx

x!(2)

where P (x) is the probability of finding x trees in a quadrat. mis the mean number of trees in a quadrat. In order to avoid overly

Fig. 2. Projections of tree crown and background. (a) Projection area ta ofa tree crown in the sunlight or viewer direction. (b) Projection area S of thesloping background in the sunlight or viewer direction. The arrow directionsare the sunlight or viewer directions.

populated quadrats that could be difficult to handle numerically,Chen and Leblanc [27] gave an example: For a 100 × 100 mdomain with 3000 trees, it is preferable to divide the domaininto at least ten quadrats.

The Neyman type-A distribution assumes that trees are firstcombined in clusters, and the spatial distribution of the centerof a cluster follows the Poisson process, that is

PN (i;m1;m2) = e−m1mi

2

i!

∞∑j=1

[m1e−m2 ]

j

j!· ji

i = 0, 1, 2, · · · (3)

where PN (i;m1;m2) is the probability of finding i trees ina quadrat, m1 is the mean number of clusters per quadrat,m2 is the cluster mean size, and j is the cluster number in aquadrat.

The tree crown distribution on sloping terrains is assumed tobe the same as that on a flat terrain at nadir, and the number oftree crowns projected in the vertical direction is assumed to beinvariant on different slopes.

C. Projection of Tree Crowns on the Sloping Background

In GO models, a tree is generally assumed to be an ideal3-D geometric shape according to the geometric characteristicsof tree species, such as cone [1], [32], ellipsoidal [28], [40],and “cone + cylinder” [27]. Rautiainen et al. [41] indicatedthat the shape of tree crowns is one of the key parameters fordetermining the canopy bidirectional reflectance. The “cone +cylinder” shape is used in GOST for coniferous tree crowns.However, other geometric shapes can also be used to replace itas needed.

The projection of tree crowns on the background is the basisto model the scene components using a GO approach. Forthe purpose of designing the new projection relationship, the“cone + cylinder” projected area ta [see Fig. 2(a)] and slopingbackground projected area S [see Fig. 2(b)] in the viewerand sunlight directions should be considered. Therefore, treecrowns are projected onto the sloping background in GOSTusing ta/S in the sunlight and view directions, separately.


Fig. 3. Topographic effects on the gap size. (a) If the sunlight or view directionis facing the sloping background, the gap fraction and gap size between crownsincrease with the increasing slope. (b) If the sunlight or viewer direction isnot facing the sloping background, the gap fraction and the gap size betweencrowns decrease with the increasing slope.

The “cone + cylinder” projected area in the view direction is

ta (θ′v) =

⎧⎨⎩

πr2 + 2r sin (θ′v)Hb θ′v = 0πr2 cos (θ′v) + 2r sin (θ′v)Hb θ′v < απr2 cos (θ′v) + tact + 2r sin (θ′v)Hb θ′v > α

(4)

where r is the radius of the tree crowns, Hb is the height ofcylinders, α is the half apex angle, and tact is the top partof the tree crown projected area in the view direction (seethe Appendix). Using θ′s instead of θ′v , (4) gives the “cone +cylinder” projected area in the sunlight direction.

The projected sloping quadrat area in the view direction is

S = A · cos(θv)/ cos(θg) (5)

where A is the projected quadrat area at nadir, and A/ cos(θg)is the sloping background area. Using θs instead of θv , (5) givesthe projected sloping area in the sunlight direction.

D. Separating Foliage and Background on Sloping Terrains

The gap fraction is used to separate foliage and backgroundon sloping terrains in GOST. In forest canopies, leaves areclumped within tree crowns, and trees are grouped ratherthan randomly distributed. Therefore, the gap fraction withina canopy is composed of those between and within treecrowns.

Fig. 3 shows that the gap fraction of a canopy is stronglyinfluenced by sloping terrains. The new projection ta/S is usedfor calculating the gap fraction between crowns on slopingterrains. In the view direction, the gap fraction between crownsin a sloping quadrat is described using the Poisson distribu-tion, i.e.,

Pvg_r =

[1− ta (θ

′v)

S

]D/n

(6)

and the gap fraction between crowns calculated usingthe Neyman type-A distribution PN (i;m1;m2) on slopingterrains is

Pvg_c =k∑

i=0

PN (i;m1;m2)

[1− ta (θ

′v)

S

]i(7)

where D is the number of trees in domain B, n is the numberof quadrats in domain B, and k is an integer that should belarge enough to consider all overlapped trees in a quadratand is equal to 350 here. Using θ′s instead of θ′v, (6) and (7)give the gap fractions between crowns corresponding to thePoisson (Pig_r) and Neyman type-A (Pig_c) distributions inthe sunlight direction, separately.

Lambert–Beer’s law is generally used for describingthe transmission of beam radiation [42]–[44]. Chen andLeblanc [27] used an equation similar to that used by Li andStrahler [35] but modified it to consider the foliage clumpingeffect [45] for simulating the gap fraction within a tree. InGOST, the function used in the four-scale model to calculategap fraction for a tree is modified. Different from the gapfractions between tree crowns, the gap fraction within a treedoes not change with the slope of the background. Therefore,the gap fraction in a tree in the view direction is

Pgap (θ′v) = e−G(θ′

v)L0ΩE/γE (8)

where G(θ′v) is the projection of unit leaf area, which is equalto 0.5 for a spherical leaf angle distribution [27], [46]. ΩE isthe clumping index for shoots, quantifying clumping at scaleslarger than the shoot. γE is the ratio of half total needle areain a shoot to half total shoot surface area [46]. L0 is the LAIin the view direction and calculated as L0 = μ · s, where μis the foliage volume density (μ = L/[V ·D/B]). For slopingterrains considered here, L is defined as one half the total leafarea per unit horizontally projected ground surface area (LAI).Therefore, according to the assumption that the tree crownis vertically grown, LAI does not change with the slope ofbackground at nadir. B is the vertically projected domain areaat nadir, and V is the volume of a tree crown. s is the mean ofpath length through a tree. In the view direction, it is calculatedas s(θ′v) = V/ta(θ

′v).

The total gap fraction over a sloping terrain is

Pvg =k∑

j=1

Ptj(ta)Pjgap (θ

′v) + Pvg_c (9)

where P jgap(θ

′v) is the gap probability within a canopy with j

trees overlapping along the view line and calculated as

P jgap (θ

′v) =

j∏1

Pgap (θ′v) . (10)

In (9), Ptj(ta) is the probability of j trees intercepting the viewline and calculated using the binomial distribution, i.e.,

Ptj(ta) =k∑

i=j

PN (i;m1;m2)i!

(i− j)!j!

×[1− ta (θ

′v)

S

]i−j [ta (θ

′v)

S

]j. (11)

With θ′s instead of θ′v, (9) can also be used to calculate thegap fraction in the sloping canopy in the sunlight direction Pig.


E. Separating Sunlit and Shaded Backgrounds onSloping Terrains

Pig represents the sunlit background fraction, and Pvg is theviewed background fraction. If the view line and solar beampenetrations through the canopy are independent of each other,the fraction of sunlit background in the view direction is simplythe product of Pig and Pvg. However, when the view line isnear the solar beam direction, it can penetrate through the samegap in the canopy as the solar beam and increases the probabil-ity of observing the sunlit background. A hotspot occurs whenthe view line is in the same direction as the solar beam. Chenand Leblanc [27] proposed a hotspot function on a horizontalsurface. In GOST, the form of the hotspot function is the sameas that of the four-scale model. However, some variables aremodified here to be suitable for sloping terrains. The hotspotfunction is

Ft(ξ) =

∫∞λmin

[1− ξ

tan−1(λ/H)

]Nt(λ)dλ∫∞

λminNt(λ)dλ

(12)

where the angle between the sun and the viewer (phaseangle) is

ξ = arccos (cos (θ′v) cos (θ′s) + sin (θ′v) sin (θ

′s) cos(φsv)) .

(13)

H is the effective height given as (Ha +Hb +Hc/3)×cos(θg)/ cos(θs), Ha is the height of the lower part of the tree(trunk space), Hb is the height of cylinders, and Hc is the heightof cones.Nt(λ) is the gap number density given as

Nt(λ) =Lt

Wte−Lt[1+(λ/Wt)]. (14)

The characteristic mean width of a tree projected in thesunlight direction is

Wt =√

ta (θ′s). (15)

The clumping-adjusted projected crown area index on slop-ing terrains is

Lt = Ωtta (θ′s)D/ (B cos(θs)/ cos(θg)) . (16)

Ωt is a tree clumping index, determined by the Neymandistribution defined as

Ωt = log (Pig_c(Neyman)) / log (Pig_r(Poisson)) . (17)

For a given angle difference between the sun and the viewer,there is a minimum gap size λmin in which the view line pe-netrates through the same gap as the solar beam, determined by

λmin = H tan(ξ). (18)

λ is the gap size of the canopy between λmin and ∞.Therefore, the total probability of seeing the sunlit back-

ground on sloping terrains is

PG = PigPvg + [Pig − PigPvg]Ft(ξ). (19)

The first term on the right-hand side represents the probabilityof observing the sunlit background when the view line pene-tration is independent of the solar beam penetration, and thesecond term is the enhanced probability due to the hotspot.

The probability of seeing the shaded background on slopingterrains is

ZG = Pvg − PG. (20)

It is the difference in the probabilities of observing the totalbackground (Pvg) and the sunlit background (PG).

F. Separating Sunlit and Shaded Foliage on Sloping Terrains

The separation of sunlit and shaded foliage in the viewdirection presents a challenge in forest GO modeling. There isstill no perfect geometric description for this purpose. In GOST,a simplified ray tracing method is developed for separatingsunlit and shaded foliage on sloping terrains. The basic ideaof this method is first to describe the foliage spatial and angulardistributions and then to penetrate a view line into the canopy.If the view line can touch any foliage in the canopy, we need todetermine whether the sunlight can reach the same point of thefoliage. Through repeating these aforementioned steps manytimes, the probability of viewing sunlit foliage can be separatedfrom the viewed foliage.

A variety of foliage shapes and crown shapes can be used forseparating sunlit and shaded foliage using straightforward geo-metric formulas of the simplified ray tracing method dependingon forest types. Specific distributions of foliage and crowns canalso be used here according to the measured data in forests.However, large amounts of needle foliage of conifer treesneed large computer memory space, which greatly exceeds thecapacity of a personal computer. For this reason, a shoot istreated as the minimum foliage element. The shape of foliagecan be treated not only to be planar shapes, such as circular,square, rectangle, rhombus, and so on, but also 3-D shapes,such as cylinder, cuboid, hexagonal prism, and so on. In orderto reduce the number of facets of a forest scene, the planarshape of foliage is used for both the broad leaved and coniferforest scenes in the simplified ray tracing method. In general,the planar shape of foliage is suitable for broadleaf forests. Forconifer forests, the projection coefficient of flat leaves in a givendirection is the same as that of spheres (representing shoots)as long as they are all randomly distributed in space, and thedefinition of half the total area is used [45]. This means that theresults of ray tracing based on the planner shape are directlyapplicable to the shoots when half of the total plane area (bothsides) is used to represent half the total shoot area (averageprojected shoot area × π). The needle-to-shoot area ratio is thenused to convert this half the total needle area to half the totalshoot area. In this way, the ray tracing results for the plannerleaf shape can be used for both broadleaf and needleleaf forests.

An example is used to explain how to use the simplified raytracing method for separating sunlit and shaded foliage. Thismethod needs to determine the forest scene on slopes first.In describing the foliage spatial and angular distributions, weassume crowns to be randomly distributed in space and leaves


to be randomly distributed within each crown. The crown isassumed to be “cone + cylinder,” and the foliage is assumedto be circular and flat plates. A vector normal to the plateis used for describing the foliage angular distribution [47].The foliage spatial distribution in a tree is expressed usingthe random centers of these plates. According to the centerand normal vector of a plate, the direction and position ofit can be determined. In the ray tracing procedure, the viewazimuth angle φv is set to zero. The sunlight direction, slopeand aspect of the terrain, and the view zenith angle θ′v are variedto simulate multiangular views. In these simulations, a plane,which is perpendicular to the direction vector of the view line,can be determined by any specific point far from the top of theforest canopy. In order to make all the view lines penetratinginto the forest scene, only a rectangle region in the plane is usedas the launch positions of the view lines according to the rangeof the forest scene. The number of the incident view lines canbe determined by the foliage density in a specific forest scene.In general, the denser the foliage in a forest scene, the moreincident view lines are required. For this reason, the number ofthe incident view lines can be related to LAI. In general, werecommend that the number of the incident view lines is no lessthan 10 000 for each forest scene, which contains no more than100 crowns with LAI of about 3. Second, the view lines are sentfrom the launch positions of the plane to the forest scene one byone. If a view line does not touch any plates in the forest scene,it is not considered. Otherwise, the first intersection point (FIP)of the view line and the plate could be found. To eliminate theedge effect, only the incident view lines that reach a relativelysmall square center area of the forest scene are preserved. Third,if the sight line intersects with a plate, we need to decidewhether the FIP can be touched by the sunlight according tothe direction vector of the sunlight and the normal vector of theplate. If there exists another plate between the sun’s positionand the FIP or the FIP is not in the same side of the plate hitby the sunlight, the FIP is a shaded point in the view direction.Otherwise, it is a sunlit point in the view direction.

After all the ray tracing procedure, we can get the percentageof sunlit points that are reached by the view lines SPT in theview direction. The total probability of seeing the sunlit foliagein the sloping canopy is

PT = SPT /(1− Pvg). (21)

The total probability of seeing the shaded foliage in thesloping canopy is

ZT = 1− Pvg − PT . (22)

III. RESULTS AND ANALYSIS

The area ratios of the four scene components of a slopingforest are conceptual quantities, which are difficult to observein real forest canopies. Therefore, the 3-D virtual canopies areconstructed using a computer graphics technique to evaluate thesimulated area ratios by GOST. Then, the reflectance simulatedby GOST is compared with the reflectance data retrieved froma TM image and from a MODIS multiangle surface reflectance

TABLE ICANOPY PARAMETERS FOR SIMULATING THE AREA RATIOS OF THE

FOUR SCENE COMPONENTS BY THE 3-D VIRTUAL MODEL AND GOST

Fig. 4. Example of a 3-D virtual canopy on a 20◦ slope. This 3-D virtualcanopy is produced using the 3-D max software and the Maxscript computerlanguage. The rendered scenes are classified as the four scene components inmultiangle directions. (a) Perspective view. (b) Nadir view. (c) Side view.

product over a mountainous area in China for the purpose ofevaluating the performance of GOST.

A. Model Comparison

In GOST, the sunlit and shaded foliage fractions that areseen in a given direction are separated based on the geometricalshape of the tree crown and the probability of solar beam andview line penetrations within the crown. The separation of thefour scene components is a fundamental part of GO modelingand is checked against ray tracing in 3-D virtual canopies.As the principles of GO modeling for broadleaf and conifercanopies are similar, we choose broadleaf virtual canopies forthis purpose, which are structurally less complex and requireless computation than conifer canopies.

1) Virtual Canopy Modeling: The 3-D max software and theMaxscript computer language are used for constructing 3-Dvirtual canopy models to compare the area ratios of the fourscene components on sloping terrains calculated using GOST.A 3-D virtual canopy consists of broad leaves that are randomlydistributed within a crown. The virtual tree crowns are dis-tributed on a sloping quadrat randomly in the vertical direction.A virtual forest scene is then separated into sunlit and shadedparts under the virtual parallel sunlight in the 3-D max cameraview. The multiangle images of the virtual canopy are renderedusing axonometric projection through moving the positions andchanging the view angles of the 3-D Max camera. Finally, thefour scene components are classified in each of the renderedmultiangle images of a virtual canopy. The regions that are notinfluenced by edge effects are artificially selected to classify thefour scene components in these rendered multiangle images.


Fig. 5. Comparison of the classified and simulated gap fractions of the sloping canopies (φg = 0) in the principal and perpendicular planes. 3D_0, 3D_10,3D_20, 3D_30, 3D_40, 3D_50, and 3D_60 are the simulated results of the 3-D virtual canopy model with the slope of the background at 0◦, 10◦, 20◦, 30◦,40◦, 50◦, and 60◦. GOST_0, GOST_10, GOST_20, GOST_30, GOST_40, GOST_50, and GOST_60 are the simulated results of GOST with the slope of thebackground at 0◦, 10◦, 20◦, 30◦, 40◦, 50◦, and 60◦.

2) Forest Site Example: A set of broadleaf canopy param-eters in reasonable ranges is shown in Table I as the inputs tothe 3-D virtual canopy model and GOST. Because it is timeconsuming to simulate the detailed forest scenes, only 1/4 ofa quadrat (125 m2) with 50 tree crowns is simulated. In thisexample, a virtual leaf is assumed to be a circular and flat platewith diameter Ws. The solar zenith angle θ′s and solar azimuthangle φs are set to 30◦ and 180◦, respectively. The azimuthangle φg of the sloping background is set to zero. An exampleof the 3-D virtual canopy on a 20◦ slope is shown in Fig. 4.

Fig. 5 shows how the gap fraction changes with backgroundslope from 0◦ to 60◦ in 10◦ intervals in the principal andperpendicular planes. The relative azimuth angle between thesun and the viewer equals 0◦ or 180◦ in the principal plane and90◦ in the perpendicular plane. The comparison shows that thegap fractions simulated by GOST agree well with the outputsfrom the 3-D virtual canopy model. It indicates the ability ofGOST to separate the foliage components and the backgroundcomponents on sloping terrains.

Different from trees growing on flat terrains, slopingcanopies cannot be observed from all view angles of the hemi-sphere (see Fig. 3). For example, the range of the view zenithangle decreases with increasing slope of the inclined back-ground in the principal plane (see Fig. 5). In the perpendicularplane, the absence of the gap fraction simulated by the 3-Dvirtual canopy model is because the tree-covered regions aretoo small to be classified in the rendered images at large θv.

Both GOST and the 3-D virtual canopy model assume thatthe number of tree crowns does not change with the slopeof terrains in the vertical direction. Therefore, the simulatedgap fraction also does not change with the slope at nadir (seeFig. 5). In the principal plane, the gap fraction increases onthe backscattering side (negative θ′v) and decreases on the for-wardscattering side (positive θ′v) with the slope of the inclinedbackground because θv values are different on both sides of thevertical direction. The gap fractions are also not the same ondifferent slopes in the same view direction. On the backscat-

tering side, the gap fraction increases with slope in the sameview direction. On the contrary, on the forwardscattering side,the gap fraction decreases with increasing slope in the sameview direction. Gap fractions on both sides of the perpendicularplane are the same because the forest scene components aresymmetric on both sides of the vertical direction when therelative azimuth angle equals 90◦. The gap fraction reachesa maximum at nadir in the perpendicular plane because theoverlapping of tree crowns is minimum in this view direction.With the increase in the view zenith angle, the overlappingof tree crowns increases, and the gap fraction decreases withslope. Moreover, the gap fraction does not change with slope ofthe inclined background at the same θ′v on both sides of theperpendicular plane because cos(φgv) = 0 and the projectedarea of background S and the projected area of a tree crownta(θ

′v) do not change with slope.

Different from the outputs of GOST, the classified gapfractions by the 3-D virtual canopy model are unsmooth (seeFig. 5). Such as the sudden rise in gap fractions at 0◦ and 10◦

slopes in the principal plane and the unsmooth gap fractions atlarge slopes in the perpendicular plane. There are also unsym-metric gap fractions that are simulated by the 3-D virtual foreston both sides of the vertical direction in the perpendicular plane.These unsmooth and unsymmetric results are caused by theinsufficient number of trees included in the simulation where afew tree crowns can have unproportionally large contributionsto the view in certain directions. However, the simulated gapfractions by GOST are smooth and symmetric both in theprincipal and perpendicular planes. This model comparisondemonstrated that the results of the 3-D virtual canopy modeland GOST have no systematic deviation, and GOST has theability to separate foliage and background area ratios (gapfraction) of forest on slopes.

The area ratios of the four scene components modeled byGOST are very close to those simulated by the 3-D virtualcanopy model in both principal and perpendicular planes (seeFigs. 6 and 7). It indicates that both models have no systematic


Fig. 6. Comparison of the classified and simulated four scene components area ratios of the sloping canopy in the principal plane. 3D_0, 3D_10, 3D_20, 3D_30,3D_40, 3D_50, and 3D_60 are the simulated results of the 3-D virtual canopy model with the slope of the background at 0◦, 10◦, 20◦, 30◦, 40◦, 50◦, and 60◦.GOST_0, GOST_10, GOST_20, GOST_30, GOST_40, GOST_50, and GOST_60 are the simulated results of GOST with the slope of the background at 0◦, 10◦,20◦, 30◦, 40◦, 50◦, and 60◦.

deviation, and GOST has the ability to separate the four scenecomponents area ratios of sloping canopies. In addition, a totalof 8500 view lines are emitted from the launching plane tothe forest scene by GOST for separating sunlit and shadedfoliage on each slope and in each view direction. The averagecomputing time for separating the four scene components isonly 8 s, and therefore, GOST is a useful method despite thefact that it contains a simplified ray tracing process. GOSTcan explicitly represent the topographic effects on area ratiosof foliage components because it considers the sloping canopystructure in any view directions. These simulations show thatthe differences in the area ratios of the four scene componentsbetween flat and sloping terrains can reach up to 50%–60% inthe principal plane and about 30% in the perpendicular plane(see Figs. 6 and 7). Therefore, without considering the effects ofsloping terrains in GO models, it might cause significant errorsin the area ratios of the four scene components, and the errorsare consequently passed to the simulated canopy reflectance.

When the view and sunlight directions are the same, the“hotspot” occurs in the principal plane (see Fig. 6). The hotspotis an important phenomenon that can be used for retrievingcanopy structural parameters, such as clumping index [8], [48].GOST successfully simulates significant increases in the area

ratios of sunlit foliage and background components at thehotspot. The shaded foliage and background area ratios are0% at the hotspot because these two scene components cannotbe observed at the hotspot. In the hotspot direction, the gapfraction increases with slope, and therefore, the sunlit andshaded foliage area ratios decrease.

The variation of the sunlit foliage area ratio reaches theminimum at different slopes at nadir at which the overlappingof tree crowns reaches the minimum. The gap fraction increaseswith slope in the backscattering side of the principal plane.Therefore, foliage area ratios decrease with increasing slope.On the contrary, the gap fraction decreases, and foliage arearatios increase with slope in the forwardscattering side. Fig. 6also shows that both the classified and simulated foliage arearatios are unsmooth in the principal plane, particularly at largeview zenith angles θv . The reason of the unsmooth resultsclassified by the 3-D virtual canopy model is the small portionof the image that can be rendered at large view zenith angles atwhich it is difficult to class the foliage area ratios. However, theunsmooth foliage area ratios simulated by GOST are causedby the small forest scene that contains an insufficient numberof trees to be statistically representative at all angles. The gapfraction increases with slope in the backscattering direction,


Fig. 7. Comparison of the classified and simulated four scene components area ratios of the sloping canopy in the perpendicular plane. 3D_0, 3D_10, 3D_20,3D_30, 3D_40, 3D_50, and 3D_60 are the simulated results of the 3-D virtual canopy model with the slope of the background at 0◦, 10◦, 20◦, 30◦, 40◦, 50◦, and60◦. GOST_0, GOST_10, GOST_20, GOST_30, GOST_40, GOST_50, and GOST_60 are the simulated results of GOST with the slope of the background at 0◦,10◦, 20◦, 30◦, 40◦, 50◦, and 60◦.

and therefore, the sunlit background area ratio increases withslope. The gap fraction does not change with slope in thenadir view direction; as a consequence, the sunlit backgroundarea ratio increases, and the shaded background area ratiodecreases with increasing slope. The sunlit background arearatio has the least influence at about 20◦ view zenith angle(θ′v). This is because the sunlit background area ratio increaseswith slope and decreases with increasing view zenith angle, andthe balance is achieved at this θ′v . In the 3-D virtual canopy,the uncertainty of the shaded background area ratio comesfrom the accumulative error because the shaded backgroundarea ratio is equal to the gap fraction minus the sunlit back-ground area ratio.

Fig. 7 also shows the unsmooth foliage area ratios classifiedby the 3-D virtual canopy model in the perpendicular plane,particularly the sudden decrease in the sunlit foliage area ratioat large θv . The sunlit background area ratio increases withslope in the perpendicular plane because more sunlight reachesthe background through a canopy. Therefore, the shaded back-ground area ratio decreases with increasing slope. In the per-pendicular plane, the gap fraction decreases with increasing θ′v,and therefore, sunlit and shaded foliage area ratios increase withθ′v. Despite the unsymmetric and unsmooth sunlit and shaded

background area ratios on both sides of the vertical direction inthe perpendicular plane, the classified background area ratiosby the 3-D virtual canopy model are close to the simulatedresults by GOST. It indicates that GOST can separate sunlit andshaded backgrounds on slopes with reasonable accuracy.

B. Model Validations

In order to prove the ability of GOST to model canopyreflectance variations with slope and aspect of the terrain,two experiments are designed for validating the reflectancesimulated by GOST. Considering the difficulty in observing thecanopy parameters on slopes, we use best estimates of commoncanopy parameters to fit the observed reflectance acquired fromremote sensing images.

1) Comparison of the Modeled and Landsat Reflectance: Inthis experiment, the reflectances of many pixels in a Land-sat TM5 image are needed to enhance the regularity of thereflectance variation with slope. Therefore, a rectangle forestregion (94 581 m × 123 375 m) northeast of China (near 53N,124E) is selected as the study site. The vegetation cover ispredominantly conifer forest in this region. The correspondingLandsat TM5 image is acquired on August 30, 2009, and


Fig. 8. Observed reflectance in the TM5 image (the red and NIR reflectance)varies with slope and aspect of the terrain. The blue, green, and red dotsrepresent the slope between 0◦ and 10◦, between 10◦ and 20◦, and between20◦ and 30◦, respectively.

a total of 3153 × 4113 nadir view pixels are selected forthis study. However, no ground observations are available forthe sloping canopy parameters corresponding to these selectedpixels. Therefore, the direct comparisons of the statistical re-sults from the Landsat TM5 image and the model simulatedresults cannot be made. In this experiment, the quantitativeanalysis of the topographical effects on the sloping canopy re-flectance is based on model simulated results, and the observedLandsat TM reflectance data are used to support the modelsimulated results.

Spectral reflectance in the red and NIR bands is retrievedfrom the original digital number of the Landsat TM5 image.The solar azimuth angle is 154◦, and the solar zenith angle is46◦ of this TM5 image. The digital elevation model (DEM)data sets for this study site are used to produce images of theslope and aspect. The slope is divided into three intervals: from0◦ to 10◦, from 10◦ to 20◦, and from 20◦ to 30◦. The aspectranges from 0◦ to 359◦ in 1◦ intervals. Then, the mean valuesof reflectance are computed for each slope and aspect interval.The statistical results of the TM5 image are shown in Fig. 8.

We have made a best estimate of the model inputs usingcommon parameter values of forest within reasonable ranges.In this case, conifer trees are simulated as “cone + cylinder”with the Neyman distribution. The slopes of 5◦, 15◦, and 25◦

are used for simulating the reflectance to represent the slopebetween 0◦ and 10◦, between 10◦ and 20◦, and between 20◦ and30◦, respectively. The other input parameters of this canopy arelisted in Table II. Then, the reflectance is simulated within theaspect range from 0◦ to 359◦ in 1◦ intervals.

Fig. 9 is the reflectance and its corresponding area ratiosof the four scene components simulated by GOST. Both thestatistical results (see Fig. 8) and the simulated results (seeFig. 9) show that the topographic factors have obvious impactson the reflectance of sloping canopies. They also show that the

TABLE IIMODEL INPUTS FOR SIMULATING THE TM REFLECTANCE

simulated reflectance by GOST compares well with that in theTM5 image with the variations of slope and aspect.

The reflectance of shaded foliage and background are as-sumed as constants because multiple scattering schemes are notyet considered in GOST. Therefore, the simulated reflectanceof sloping canopies depends on the area ratios of the four scenecomponents at different slopes and aspects. According to apreamble analysis, the gap fraction is invariant at nadir. Asa consequence, the area ratio of shaded foliage moves in theopposite direction to the area ratio of sunlit foliage at differentaspects, so does the relationship between the sunlit and shadedbackgrounds. Furthermore, the simulated reflectance of slopingcanopies depends on the area ratios of the sunlit componentsbecause the reflectance of the sunlit components is considerablylarger than those of the shaded components in both the redand NIR bands. Therefore, the simulated results by GOSTshow positive correlations between the reflectance of slopingcanopies and the area ratios of the sunlit components (seeFig. 9). The negative correlations between the reflectance ofsloping canopies and the area ratios of the shaded componentsare also shown. Although the absolute values of the observedreflectance in the TM5 image and the simulated reflectanceof GOST are different, the patterns of the angular variationsof the two results are similar, particularly in the NIR band.In the red band, the observed reflectance at slopes from 0◦

to 10◦ has no significant difference from those from 10◦ to20◦ because their specific canopy structures are not consideredin this experiment. The preamble analysis indicates that theangular variation pattern of the simulated results is compatiblewith the observed reflectance in theTM5 image (see Fig. 8).


Fig. 9. Simulated four scene components area ratios, red reflectance and NIR reflectance vary with slope and aspect of the terrain by GOST. Slope_5, Slope_15,and Slope_25 are the simulated results of GOST with the slope of the background at 5◦, 15◦, and 25◦, respectively.

Fig. 9 also shows that the area ratios of the sunlit foliage andbackground reach their maximum values, respectively, and thearea ratios of the shaded foliage and background reach theirminimum values, respectively, at certain angles on the sunlitslope. (The aspect φg is about 154◦, and the relative azimuthangle between the sun and the sloping background is about0◦.) On the contrary, the area ratios of the shaded foliage andbackground reach their maximum values and the area ratios ofthe sunlit foliage and background reach their minimum valuesat certain angles on the shaded slope. (The aspect φg is about334◦, and the relative azimuth angle between the sun and thesloping background is about 180◦.) Therefore, the maximumand minimum values of reflectance simulated by GOST in boththe red and NIR bands appear on the sunlit and shaded slopesfor each canopy, respectively. This result is supported by theobserved reflectance of the TM5 image.

Furthermore, sunlight can reach more foliage and back-ground on the sunlit slope and less foliage and backgroundon the shaded slope with the increasing slope. Therefore, thecanopy reflectance on the sunlit slope increases with slope dueto the increasing area ratios of the sunlit foliage and back-ground. On the contrary, the canopy reflectance on the shadedslope decreases with increasing slope due to the increasing arearatios of the shaded foliage and background. It indicates thatthe variation of the canopy reflectance at a steeper slope isbigger than those at a gentler slope. Both the area ratios ofthe four scene components and its corresponding reflectance areminimally affected by the topographic factors when the relativeazimuth angle between the sunlight and background aspect φsg

is about 90◦. It is because the topographic factors have the leasteffects on the area ratios of the four scene components at about

90◦ φsg. The observed reflectance also supports that biggerand smaller variations of the reflectance are caused by thesteeper and gentler slopes, respectively, and the reflectance isminimally affected by the topographic factors at about 90◦ φsg

(see Fig. 8).The dynamic range of the simulated reflectance is smaller

than that in the remote sensing image. This is because 1) thesimulation of GOST in this case only considers the topograph-ical variations rather than the variations of canopy parameters,such as LAI and 2) the reflectance of the shaded foliage andbackground are assumed to be constants in GOST. However,with the support of the observed reflectance in the TM5 image,the simulated results suggest that GOST can capture the majorangular variation of the reflectance of sloping canopies.

2) Comparison of the Modeled and MODIS MultiangleSurface Reflectance: In order to further prove the ability ofGOST to simulate sloping forest reflectance, an experiment isdesigned for comparing the simulated multiangle reflectance byGOST with the MODIS surface reflectance. In this experiment,the simulated reflectances with or without considering thetopographic factors are compared against MODIS multianglesurface reflectance.

MODIS MOD09GA reflectance data at the 500-m spatialresolution are used for this purpose. A sloping forest locationis selected according to slope and aspect maps generated usingDEMs downloaded from the U.S. Geological Survey. Cloud-free reflectance values in the red and NIR bands over the courseof one month at this location as well as the correspondingsolar and view angular data with 1-km spatial resolution arecollected for evaluation purposes. The study site is locatedin Chongqing City, China (29◦37′18.12′′N/107◦22′47.28′′E).


TABLE IIIMODEL INPUTS FOR SIMULATING THE MULTIANGLE

MODIS SURFACE REFLECTANCE

Pine (Pinus massoniana) is the major conifer species at thisstudy site. Nine cloud-free days from August 1 to 31 of 2011are selected. The slope is 20◦ and aspect is 89◦ from the north.

The input parameters of GOST for this sloping canopy arelisted in Table III. In fact, it is difficult to give observation datasets exactly for these 250 000 m2 (500-m spatial resolution)pixels in the remote sensing images. We have made a best guessto determine the model input using common parameter valuesof forest within reasonable ranges. The same input parametersare used to simulate the reflectance using GOST with or withoutconsidering topographic factors. Therefore, the differences ofthese modeled results are not derived from these input canopyparameters.

Within these nine cloud-free MODIS observations, thereexist one kind of combination of the view azimuth angle, solarazimuth angle, and solar zenith angle. The combination isthat the view azimuth angles approximately equaling 95◦, thesolar azimuth angles approximately equaling 121◦, and solarzenith angles approximately equaling 27◦. The variation ofthe view zenith angle is from 1◦ to 62◦. Therefore, with orwithout considering topographic factors, reflectance values inthis plane are simulated according to this angle combinationand compared with the MODIS multiangle surface reflectance.

Fig. 10 shows the comparison between the simulated re-flectance and MODIS surface reflectance in the red and NIRbands. Generally, the MODIS surface reflectance is closer to thesimulated reflectance with considering the topographic factors(slope is 20◦) than those without considering the topographic

Fig. 10. Simulated multiangle reflectance compared with MODIS surfacereflectance at multiple view angles in the red and NIR band. Slope_0 andSlope_20 are the simulated results of GOST with the slope of the backgroundat 0◦ and 20◦, respectively.

factors (slope is 0◦). The dynamic range of the simulatedreflectance with considering the topographic factors is close tothat of the observed results. However, the dynamic range ofthe simulated reflectance without considering the topographicfactors is underestimated in the red band and overestimatedin the NIR band. In the red band, the simulated reflectancewithout considering the topographic factors is also underesti-mated. However, it is overestimated in the NIR band at largeview zenith angles (view zenith angles larger than 30◦). Thesimulated reflectance with considering the topographic factorsappears within reasonable ranges. However, there are still slightdifferences between the simulated reflectance and MODISsurface reflectance after considering the topographic factors.This can be related to inexact angular matching between themodel and the observation, and the approximation of the com-plex topographical variations within the 500-m pixels with2-D (smooth and extensive) slopes. This comparison furtherconfirms the ability of GOST in simulating the multianglereflectance of sloping canopies.

IV. CONCLUSION

Based on the four-scale GO model developed for flat terrains,the GOST model in this study is developed to describe theeffect of the sloping canopy structure on the reflectance. Thefollowing conclusions are drawn from this study.

1) GOST is able to simulate the gap fraction and the ra-tios of the four scene components (sunlit and shadedcanopy fractions and sunlit and shaded background frac-tions) on sloping terrains. The simulation compares wellwith the 3-D virtual canopy using a computer graphicstechnique.

2) GOST provides a useful tool for analyzing remotesensing images over complex terrains. It considerablyimproves the simulated reflectance in a mountainousarea after considering the topographic factors. Model


Fig. 11. Projection area tact in the sunlight or viewer directions. tact is in thetop part of the “cone + cylinder.” A(xa, ya), B(xb, yb), and D(xd, yd) areused for calculating projection area tact.

evaluations against Landsat and MODIS observationsdemonstrate that the simulated reflectance of GOST oversloping terrains does not have obvious systematic biases.The evaluation against MODIS data also suggests thatGOST can simulate multiangle reflectance on slopingforests.

Although it can be improved to include a within-canopymultiple scattering scheme, GOST presented here already has aunique ability to model the bidirectional reflectance distributionof vegetation over sloping terrains. It can also be a useful toolfor retrieving canopy parameters using remote sensing imageson complex terrains.

APPENDIX

tact GEOMETRY

Projection area tact can be computed by integrating twicefrom the ellipse to segment BD from 0 to yd (see Fig. 11).Thus

tact =2

yd∫0

(y − bBD

mBD− xa

r

√r2 − y2

)dy

=2xb · yd −y2d ·

√x2b − x2

a

r

− xa

r

[yd ·

√r2 − y2d + r2 · arcsin

(ydr

)](23)

where bBD is the intercept of segment BD, and mBD is theslope of segment BD. xa, xb, and yd can be calculated asfollows: ⎧⎪⎨

⎪⎩xa = r · cos (θ′v)xb = r · sin (θ′v) / tan(α)yd = r ·

√x2b−x2

a

xb.

(24)

ACKNOWLEDGMENT

The authors would like to thank Dr. Z. Y. Tong andDr. G. Zheng from Nanjing University, for their help in 3-Dvirtual modeling. They would also like to thank the two review-ers for their substantial comments.

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Weiliang Fan received the B.S. degree in hor-ticulture from Shandong Agricultural University,Shandong, China, in 2007 and the M.S. degree inforest management from Zhejiang A&F University,Zhejiang, China, in 2010. He is currently work-ing toward the Ph.D. degree at Nanjing University,Jiangsu, China.

Jing M. Chen received the B.Sc. degree from theNanjing Institute of Meteorology, Nanjing, China, in1982 and the Ph.D. degree from Reading University,Reading, U.K., in 1986.

He is a Professor with the Department of Geogra-phy and Program in Planning, University of Toronto,Toronto, ON, Canada; a Canada Research Chair; anda Fellow of the Royal Society of Canada. He isalso an Adjunct Professor with Nanjing University,Nanjing. He has published over 200 papers in refer-eed journals, which have been cited over 5000 times

in the scientific literature. His major research interests include remote sensingof vegetation and quantifying terrestrial carbon and water fluxes.

Dr. Chen is currently an Associate Editor of the Journal of GeophysicalResearch-Atmosphere, Canadian Journal of Remote Sensing, and Journal ofApplied Remote Sensing.

Weimin Ju received the B.Sc. degree from theNanjing Institute of Meteorology, Nanjing, China,in 1984 and the M.Sc. and Ph.D. degrees from theUniversity of Toronto, Toronto, ON, Canada, in 2002and 2006, respectively.

He is currently a Professor with the InternationalInstitute for Earth System Sciences, Nanjing Uni-versity, Nanjing. He has published over 80 papersin refereed journals, including 45 papers in interna-tional journals. His major research interests includeretrieval of vegetation parameters from remote sens-

ing data and simulating terrestrial carbon and water fluxes.

Gaolong Zhu received the B.S. degree in geogra-phy from Beijing Normal University, Beijing, China,in 1997; the M.S. degrees in cartography and ge-ographic information system (GIS) from PekingUniversity, Beijing, in 2003; and the Ph.D. degreein cartography and GIS from Nanjing University,Nanjing, China, in 2011.

He is currently an Associate Professor withthe Department of Geography, Minjiang University,Fuzhou, China. His current research interests in-clude modeling and inversion of multiangular remote

sensing data.

Documents

GOST: A Geometric-Optical Model for Sloping Terrainsfaculty.geog.utoronto.ca/Chen/Chen's homepage... · 2000s withtheaddition of radiative transferschemes toaddress the complex multiple